Problem: $J$ is the midpoint of $\overline{CT}$ $C$ $J$ $T$ If: $ CJ = 8x - 5$ and $ JT = 9x - 9$ Find $CT$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${CJ} = {JT}$ Substitute in the expressions that were given for each length: $ {8x - 5} = {9x - 9}$ Solve for $x$ $ -x = -4$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $CJ$ and $JT$ $ CJ = 8({4}) - 5$ $ JT = 9({4}) - 9$ $ CJ = 32 - 5$ $ JT = 36 - 9$ $ CJ = 27$ $ JT = 27$ To find the length $CT$ , add the lengths ${CJ}$ and ${JT}$ $ CT = {CJ} + {JT}$ $ CT = {27} + {27}$ $ CT = 54$